I don't know why, but I love this topic.
Considering only the classic Satellite JLA, and considering the most populated countries on the planet:
Superman - India, totes. Raised in poverty by humble farmers. Living lives in two different castes.
Batman - Mexico. A country with plenty of innocents to protect in never-ending war against crime. Also, Zorro.
Wonder Women - Brazil. It's working really well in Wonder Girl right now.
J'Onn J'Onnz - African American. He's arguably more emblematic of the modern American immigrant experience than Superman these days, so he's the token US citizen.
Flash - Ethiopian. I bit cliche, but an African Flash seems like a cool thing.
GL - Pakistan. Perhaps even go the full "jet fighter who refuses to kill innocents" route.
Green Arrow - China. A perpetual thorn in the side of the Communist Party, ironically.
Atom - Indonesia.
Aquaman - Philippines. Atlantis would be more of a Pacific Ocean kingdom.
Hawkman and Hawkwoman - Egypt (duh). If you wanted to get saucy, the current incarnation of Shayera could be Israeli, but that's a bit on-the-beak.
Black Canary - Japan.
Red Tornado - Russia.
Firestorm - German. A fusion of a native German professor and an immigrant teenager.
Zatanna - Bangladesh. Remarkably close to the hidden land of the Homo Magi.
Elongated Man - Nigeria. I liked the idea of a master detective from Nigeria.
They'd have to all learn Interlac, I suppose
I liked Ducklord's list. It was really inventive, especially considering some heroes that I had forgotten.
I think a hero from Turkey would be a good idea too. But I can't think of a good fit.
Turkey's in the Top 20 in world population, so they'd be a reasonable fit. Frankly, making Firestorm German was a bit of a cheat, as I kind of used him as a proxy for the whole EU (Germany's 19th in World Pop, behind Vietnam, the Congo, Turkey, and Iran). One could EASILY make Firestorm Iranian (an accident in an experimental Iranian enrichment facility, perhaps).
It's purely my European-descended whiteguyness that makes me balk at an international JLA with no European representation, even though, statistically, that's not where the people are at
Wonder Woman, most definitely. Some say Themiscyra is in Black Sea region of the country.
https://www.allaboutturkey.com/amazon.html
https://www.ephesus.us/mythologies/amazons.htm
https://www.tourmakerturkey.com/amazon-village.html
The Amazon myths were said to be inspired by the Scythians who were said to resemble modern day Iranians. So WW could resemble Iranians. Steve Trevor could be from Iran in this version.
Zatanna could be dual Italian and Turkish. Father is from Italy and her mother Sindella is canonically from the Hidden City of Turkey.
Raven could be from India since Perez/Wolfman used a lot of Hindu motifs when drawing her costumes in NTT and even drew her in a sari at one point.
Always thought an Asian Bruce Wayne could work (even though I don't think the the YA novel really nailed it), parents could be a well off but not uber wealthy doctor from Singapore. They walk into crime alley because they were unfamiliar with the city. His drive could come from his parents trying to push him towards excellence, his training could just be part of him reconnecting with his roots and Ras could be an international crime lord whose business who takes an interest in Bruce because his business is being taken apart by the Batman. You could base him in either Hong Kong or Thailand entirely if you want to keep him entirely non American.
Catwoman: Egyptian with the cat motif being inspired by the Goddess Bast.